List of top Mathematics Questions on Distance between Two Lines asked in KEAM

The shortest distance between the straight line \[ \vec{r} = 3\hat{i}+12\hat{j}+5\hat{k} +\lambda(2\hat{i}), \qquad \lambda\in\mathbb{R}, \] and the \(x\)-axis is:

The shortest distance between the lines $\vec{r}=\hat{i}+\hat{j}+3\hat{k}+\lambda(2\hat{i}+2\hat{j}+\hat{k})$ and $\vec{r}=(2\mu+1)\hat{i}+(2\mu-1)\hat{j}+(\mu+1)\hat{k}$ where $\lambda$ and $\mu$ are parameters, is

The shortest distance between the lines $\vec{r} = -\hat{i} + t\hat{k}, \; t \in \mathbb{R}$ and $\vec{r} = -\hat{j} + s\hat{i}, \; s \in \mathbb{R}$ is:

The shortest distance between the point \( (2,3,4) \) and the line \( \dfrac{x-4}{-2}=\dfrac{y-4}{2}=\dfrac{z-6}{1} \) is

Distance between two parallel lines \( y = 2x + 4 \) and \( y = 2x - 1 \) is

Let \( \overrightarrow{OB} = \hat{i} + 2\hat{j} + 2\hat{k} \) and \( \overrightarrow{OA} = 4\hat{i} + 2\hat{j} + 2\hat{k} \). The distance of the point \( B \) from the straight line passing through \( A \) and parallel to the vector \( 2\hat{i} + 3\hat{j} + 6\hat{k} \) is